Measurement of the Absolute Branching Fractions B to Dpi, D*pi, D**pi with a Missing Mass Method

We present branching fraction measurements of charged and neutral B decays to Dpi-, D*pi- and D**pi- with a missing mass method, based on a sample of 231 million Y(4S)-->BBar pairs collected by the BaBar detector at the PEP-II e+e- collider. One of the B mesons is fully reconstructed and the other one decays to a reconstructed charged pion and a companion charmed meson identified by its recoil mass, inferred by kinematics. Here D** refers to the sum of all the non-strange charm meson states with masses in the range 2.2-2.8 Gev/c2.

We present branching fraction measurements of charged and neutral B decays to D π − , D * π − and D * * π − with a missing mass method, based on a sample of 231 million Υ (4S) → BB pairs collected by the BABAR detector at the PEP-II e + e − collider. One of the B mesons is fully reconstructed and the other one decays to a reconstructed charged π and a companion charmed meson identified by its recoil mass, inferred by kinematics. Here D * * refers to the sum of all the non-strange charm meson states with masses in the range 2.2 − 2.8 GeV/c 2 . We measure the branching fractions: The first uncertainty is statistical and the second is systematic. Our understanding of hadronic B-meson decays has improved considerably during the past few years with the development of the Heavy Quark Effective Theory (HQET) [1,2] and the Soft Collinear Effective Theory (SCET) [3,4]. In these models, and in the framework of the factorization hypothesis [4,5], the amplitude of the B → D ( * ) π two-body decay carries information about the difference δ between the strong-interaction phases of the two isospin amplitudes A 1/2 and A 3/2 that contribute [6,7]. A non-zero value of δ provides a measure of the departure from the heavy-quark limit and the importance of the final-state interactions in the D ( * ) π system. With the measurements by the BABAR [8] and BELLE [9] experiments of the color-suppressed B decay B 0 → D ( * )0 π 0 providing evidence for a sizeable value of δ, an improved measurement of the color-favored decay amplitudes (B − → D ( * )0 π − and B 0 → D ( * )+ π − ) is of renewed interest. In addition, the study of B decays into D, D * , and D * * mesons will allow tests of the spin symmetry [10,11,12,13] imbedded in HQET and of nonfactorizable corrections [14] that have been assumed to be negligible in the case of the excited states D * * [15].
In this paper we present new measurements of the branching fractions for the decays B − → D 0 π − , D * 0 π − , D * * 0 π − , and B 0 → D + π − , D * + π − , D * * + π − [16], based on a missing mass method previously used by BABAR [17]. Here D * * refers to the sum of all the non-strange charm meson states with masses in the range 2.2 − 2.8 GeV/c 2 . This analysis uses Υ (4S) → BB events in which a B + or a B 0 meson, denoted B reco , decays into a hadronic final state and is fully reconstructed. The decays of the recoiling B into a charged pion and a charmed meson, i.e. B → π − X, are studied. The charged pion is reconstructed and the mass of the X = D, D * , D * * is inferred from the kinematics of the two body B decay. This method, unlike the previous exclusive measurements [18,19], does not assume that the Υ (4S) decays into B + and B 0 with equal rates, nor does it rely on the D, D * , or D * * decay branching fractions.
The measurements presented here are based on a sample of 231 million BB pairs (210 fb −1 ) recorded at the Υ (4S) resonance with the BABAR detector at the PEP-II asymmetric-energy B factory at SLAC. The BABAR detector is described in detail elsewhere [20]. Chargedparticle trajectories are measured by a 5-layer doublesided silicon vertex tracker (SVT) and a 40-layer drift chamber (DCH), both operating in a 1.5-T solenoidal magnetic field. Charged-particle identification is provided by the average energy loss (dE/dx) in the tracking devices and by an internally reflecting ring-imaging Cherenkov detector. Photons are detected by a CsI(Tl) electromagnetic calorimeter. Muons are identified by the instrumented magnetic-flux return (IFR). We use Monte Carlo (MC) simulations of the BABAR detector based on GEANT4 [21] to optimize selection criteria and determine selection efficiencies.
We reconstruct B + and B 0 decays (B reco ) in the modes B + → D ( * )0 π + , D ( * )0 ρ + , D ( * )0 a + 1 , and B 0 → D ( * )− π + , D ( * )− ρ + , D ( * )− a + 1 . D 0 candidates are reconstructed in the K + π − , K + π − π 0 , K + π − π + π − , and K 0 S π + π − decay channels, while D − candidates are reconstructed in the K + π − π − and K 0 S π − modes, and K 0 S mesons are reconstructed to π + π − . D * candidates are reconstructed in the D * − → D 0 π − and D * 0 → D 0 π 0 decay modes. A 3σ cut is applied on the D meson mass m D (and on the D * -D mass difference ∆m D * ) where σ = σ mD (σ ∆m D * ) is the resolution on m D (∆m D * ) and is determined from data. A vertex fit is performed on D (D * ) with the mass constrained to the nominal value [22]. Two nearly independent variables are defined to identify the fully reconstructed B candidates kinematically. The first one is the beam-energy substituted mass, is the four-momentum of the initial e + e − system, both measured in the laboratory frame. The invariant mass of the initial e + e − sys- is the B reco candidate energy in the centerof-mass frame. To define the B reco sample ( Fig. 1), we require |∆E| < n σ ∆E , where the measured resolutions σ ∆E range from 12 to 35 MeV and n = 2 or 3, both depending on the B reco mode. The B reco candidate multiplicity is 1.4 for data as well as for the MC simulation sample. For events with more than one candidate, we select the B reco with the best χ 2 defined with the variables m D , ∆m D * , and ∆E. The MC simulation shows that the recoil variables are reconstructed well within their experimental resolution when using this selection.
The number of B reco is extracted from the m ES spectra ( Fig. 1) in the 5.27 − 5.29 GeV/c 2 signal region. The m ES distribution is fit to the sum of a broad combinatorial background and a narrow signal in the mass interval 5.21 − 5.29 GeV/c 2 . The combinatorial background is described by an empirical phase-space threshold function [23] and the signal with a Crystal Ball function [24] which is a Gaussian function centered at the B meson mass modified to account for photon radiation energy-loss. All parameters for the functions describing the B reco signal and background distributions are determined from data. The measured yields of reconstructed B + and B 0 candidates, N B + = 189474 ± 7487 and N B 0 = 103169 ± 3303, are obtained by subtracting the fitted and the peaking (described below) backgrounds from the total number of events found in the signal region. These B reco numbers serve as the normalization of all branching fraction measurements reported in this paper. The error is dominated by the systematic uncertainties due to the fit of the combinatorial background and to the determination of the peaking background. We assign 2.3% uncertainty to N B + and 1.8% to N B 0 as a fit uncertainty, obtained by varying the lower boundary of the fit interval from 5.20 to 5.23 GeV/c 2 . The contamination of misreconstructed B 0 events in the B + signal (and vice-versa) induces a peaking background near the B mass. From the MC simulation, the fraction of B 0 events in the reconstructed B + signal sample is found to be (3.2 ± 3.2 syst. )% and the fraction of B + events in the reconstructed B 0 signal sample (2.8 ± 2.8 syst. )%. A 100% systematic uncertainty is conservatively assigned to these numbers taking into account the possible differences in the reconstruction efficiency in data and MC, as well as the branching fraction uncertainties for those B decay modes contributing to the peaking background. The total systematic uncertainties on N B + and N B 0 are 3.9% and 3.2%, respectively.
In the decay Υ (4S) → B reco B Xπ where B Xπ is the recoiling B which decays into π − X, the invariant mass of the X system is derived from the missing 4-momentum p X applying energy-momentum conservation: The 4-momentum of the Υ (4S), p Υ (4S) , is computed from the beam energies and p π − and p Breco are the measured 4-momenta of the pion and of the reconstructed B reco , respectively. The B reco energy is constrained by the beam energies. The B → Dπ − , B → D * π − , or B → D * * π − signal yields peak at the D, D * , and D * * masses in the missing mass spectrum, respectively.
The pion candidates, chosen among the tracks that do not belong to the B reco , are required to have produced at least 12 DCH hits. For the charged B reco , the pion candidate has the opposite sign to the B reco . For neutral B reco , because of the B 0 −B 0 mixing, the corresponding requirement is not applied. Muon tracks are rejected using the IFR information, electrons tracks using the energy loss in the SVT and the DCH, or the ratio of the candidate's EMC energy deposition to its momentum (E/p). Protons and kaons are rejected based on informations from the DIRC and energy loss in the SVT and the DCH. The rejection efficiency is 97% and there is no peaking trend in the missing mass distribution from remaining kaons, protons, muons, or electrons. The pion reconstruction efficiency is determined from the MC simulation and reported in Table I.
The signal yields for the different decay modes are extracted from the missing mass spectra. The data distributions and the bb and the qq (q = c, u, d, s) background expectations are shown in Figs. 2(a) and 2(b). The shape of the background is taken from MC and the normalization is scaled to match the data in the sideband region 2.8 − 3.2 GeV/c 2 . The error on the background normalization is 2%. This is determined using the statistical errors of MC and data samples. The background subtracted missing mass distributions are shown in Figs. 2(c) and 2(d).
The Dπ and D * π signal yields are extracted by a χ 2 fit to the background subtracted missing mass distribution in the range 1. are fixed to 0.1421 GeV/c 2 and to 0.1406 GeV/c 2 for B + and B 0 , respectively, corresponding to the world average D and D * mass differences [22].
The D * * yields are defined as the excess of candidates in the missing mass range 2.2 − 2.8 GeV/c 2 , and the B → D * * π − branching fractions refer to the contributions of all non-strange charm meson states in the same region. The range is chosen in order to maximize the acceptance to the four P-wave D * * states predicted by the theory given the 34 MeV/c 2 mass resolution, determined from MC simulation, in the same region. The well-known narrow D 1 and D * 2 states [22] are fully contained in this range, and more than 90% of the broad D 0 and D ′ 1 , are covered if measured masses and widths [25,26] are used. The event yields, the efficiencies, and the resulting branching fractions are reported in Table I.
The uncertainty related to π reconstruction efficiency is due to the MC sample statistics and the systematic uncertainty on track reconstruction and particle iden- I: Signal yields, efficiencies and branching fractions for B → Dπ − , B → D * π − and B → D * * π − . The first error is statistical except for the efficiencies for which it is mainly systematic. The second error on the branching fractions is systematic. The B → D * * π − branching fractions are given for the 2.2 − 2.8 GeV/c 2 mass range which in addition to the P-wave states may include some yet unknown charm meson states. Decay mode Yield Efficiency tification algorithms. The uncertainty due to the yield extraction is estimated by fitting the MC sample. The difference between the MC and the data fitted yields is found to be consistent with zero and the statistical errors are taken as a systematic error. We evaluate the uncertainty on the missing mass resolution in the Dπ and D * π yield extraction by varying by one standard deviation the ratio σ D * i /σ D i while σ D * 2 and m D * 2 are let free. The difference in the yield is taken as systematic uncertainty. The uncertainty related to the subtraction of the background is determined by varying the branching fraction of the different background components within the uncertainties of the most recent measurements [22] and taking into account the error on the background normalization. Due to the threshold shape of some of the background components and the fast varying combinatorial background, B → D * * π branching fractions have larger systematic errors than B → Dπ and B → D * π branching fractions. The summary of these systematic uncertainties is reported in Table II.
Using the measured branching fractions we compute the following ratios: The first uncertainty is statistical and the second is systematic. In addition to the cancellation of many of the systematic errors, the ratios are insensitive to the absolute normalization scale.
We are grateful for the extraordinary contributions of our PEP-II colleagues in achieving the excellent luminosity and machine conditions that have made this work possible. The success of this project also relies critically on the expertise and dedication of the computing organizations that support BABAR. The collaborating institutions wish to thank SLAC for its support and the kind hospitality extended to them.